Best Known (43−29, 43, s)-Nets in Base 32
(43−29, 43, 120)-Net over F32 — Constructive and digital
Digital (14, 43, 120)-net over F32, using
- t-expansion [i] based on digital (11, 43, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(43−29, 43, 146)-Net over F32 — Digital
Digital (14, 43, 146)-net over F32, using
- net from sequence [i] based on digital (14, 145)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 14 and N(F) ≥ 146, using
(43−29, 43, 150)-Net in Base 32 — Constructive
(14, 43, 150)-net in base 32, using
- 321 times duplication [i] based on (13, 42, 150)-net in base 32, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
(43−29, 43, 161)-Net in Base 32
(14, 43, 161)-net in base 32, using
- 5 times m-reduction [i] based on (14, 48, 161)-net in base 32, using
- base change [i] based on digital (6, 40, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- base change [i] based on digital (6, 40, 161)-net over F64, using
(43−29, 43, 6383)-Net in Base 32 — Upper bound on s
There is no (14, 43, 6384)-net in base 32, because
- 1 times m-reduction [i] would yield (14, 42, 6384)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1646 535555 805750 215469 489047 295997 747803 613541 179055 347620 807731 > 3242 [i]